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Simplifying t2 + 15t + 10 = 0 Reorder the terms: 10 + 15t + t2 = 0 Solving 10 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 15t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + 15t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 15t + t2 = 0 + -10 15t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 15t + t2 = -10 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = -10 + 56.25 Reorder the terms: 56.25 + 15t + t2 = -10 + 56.25 Combine like terms: -10 + 56.25 = 46.25 56.25 + 15t + t2 = 46.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (t + 7.5) equal to 6.800735254 and -6.800735254.Subproblem 1
t + 7.5 = 6.800735254 Simplifying t + 7.5 = 6.800735254 Reorder the terms: 7.5 + t = 6.800735254 Solving 7.5 + t = 6.800735254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 6.800735254 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 6.800735254 + -7.5 t = 6.800735254 + -7.5 Combine like terms: 6.800735254 + -7.5 = -0.699264746 t = -0.699264746 Simplifying t = -0.699264746Subproblem 2
t + 7.5 = -6.800735254 Simplifying t + 7.5 = -6.800735254 Reorder the terms: 7.5 + t = -6.800735254 Solving 7.5 + t = -6.800735254 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -6.800735254 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -6.800735254 + -7.5 t = -6.800735254 + -7.5 Combine like terms: -6.800735254 + -7.5 = -14.300735254 t = -14.300735254 Simplifying t = -14.300735254Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.699264746, -14.300735254}
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